# ---
# title: 1373. Maximum Sum BST in Binary Tree
# id: problem1373
# author: Tian Jun
# date: 2020-10-31
# difficulty: Hard
# categories: Dynamic Programming, Binary Search Tree
# link: <https://leetcode.com/problems/maximum-sum-bst-in-binary-tree/description/>
# hidden: true
# ---
# 
# Given a **binary tree** `root`, the task is to return the maximum sum of all
# keys of **any**  sub-tree which is also a Binary Search Tree (BST).
# 
# Assume a BST is defined as follows:
# 
#   * The left subtree of a node contains only nodes with keys  **less than**  the node's key.
#   * The right subtree of a node contains only nodes with keys  **greater than**  the node's key.
#   * Both the left and right subtrees must also be binary search trees.
# 
# 
# 
# **Example 1:**
# 
# ![](https://assets.leetcode.com/uploads/2020/01/30/sample_1_1709.png)
# 
#     
#     
#     Input: root = [1,4,3,2,4,2,5,null,null,null,null,null,null,4,6]
#     Output: 20
#     Explanation: Maximum sum in a valid Binary search tree is obtained in root node with key equal to 3.
#     
# 
# **Example 2:**
# 
# ![](https://assets.leetcode.com/uploads/2020/01/30/sample_2_1709.png)
# 
#     
#     
#     Input: root = [4,3,null,1,2]
#     Output: 2
#     Explanation: Maximum sum in a valid Binary search tree is obtained in a single root node with key equal to 2.
#     
# 
# **Example 3:**
# 
#     
#     
#     Input: root = [-4,-2,-5]
#     Output: 0
#     Explanation: All values are negatives. Return an empty BST.
#     
# 
# **Example 4:**
# 
#     
#     
#     Input: root = [2,1,3]
#     Output: 6
#     
# 
# **Example 5:**
# 
#     
#     
#     Input: root = [5,4,8,3,null,6,3]
#     Output: 7
#     
# 
# 
# 
# **Constraints:**
# 
#   * The given binary tree will have between `1` and `40000` nodes.
#   * Each node's value is between `[-4 * 10^4 , 4 * 10^4]`.
# 
# 
## @lc code=start
using LeetCode

## add your code here:
## @lc code=end
